I keep trying, but I can't get this.
The two solutions of the equation x^2 + bx + 18 = 0 are in the ratio of 3 to 1 for some values of b. What is the largest possible value of b?
+297 Hm.. can you explain further for the 3:1 ratio is it for the variable b or the variable x?
+297 I get it now. Okay so first, look at the constant term 18. we need some 2 numbers to be in a 3:1 ratio and multiply to get 18 so
\(xy=18\)
\(4y=x\)
from this system of equations we get
\(y = \sqrt{4.5}\)
\(x = \sqrt{72}\)
these are the 2 solutions the this quadratic.
we can express this as
\((x - \sqrt{4.5})(x-\sqrt{72}) = 0\)
so b is equal to \(\sqrt{4.5} + \sqrt{72}\)
hope this helped(i hope this is not wrong)
